IF a parent loses their parental rights, are they still responsible for child support?

I have a few friends in this situation. The mom relinquished parental rights of the father. The father is still entitled to child support. Why is this so? If a person can't see their kids or have an active role, why is monetary support still requested. I also have relative where the mother of his kids has married and now wants him to sign over his rights so that her new husband can adopt. Sighing that now he wont have to make child support payments. Can someone clear this up for me?